I think there's roughly two good strategies for having conversations with people.
The first is actually speaking your mind freely once you get to know someone even a bit, including all the politically incorrect things.
As a somewhat tame example, I think the British Empire did more good than any other nation in history and was overwhelmingly a force for good in humanity. However, people mostly hear about their bad deeds, but don't hear about all the suicide cults, assassin's organizations, human sacrificing religions, and so on, and so on, that they ended. People also take for granted all the hygiene, infrastructure, rule of law, scientific method, and so on that they propagated.
I'll point this out, even though it upsets some people. It's honest and not politically correct (but true!).
There's another strategy, which is to suss out what the person you're speaking to thinks, and try to converse on common ground and without being offensive. Done correctly, this actually means being liked by a wider group of people and not offending as many people... and this isn't so bad, really. Most people will lionize speaking up in theory, but react really hostile in practice if you say, for instance, that you think universal suffrage is a terrible way to choose a government.